Finance tools
Rule of 72 calculator
Estimate how long it takes to double your money with the Rule of 72, or find the annual return needed to double in a target number of years. See the shortcut beside the exact once-per-year compound answer, with presets, optional starting balance, and CSV/PDF export.
What is the Rule of 72?
The Rule of 72 estimates how many years it takes to double an investment: divide 72 by the annual interest rate (written as a percent). It is a quick mental-math shortcut for compound growth, not a forecast—fees, taxes, and changing returns all affect real life.
People use it to sanity-check savings APY, a rough expected portfolio return, or a finance-class problem. The math sits next to compound interest: when earnings stay invested, balance grows faster over time. For plain-language U.S. investor education on compounding, see Investor.gov’s compound interest calculator (external).
Below, you can run the shortcut both ways (years ↔ rate), add an optional starting amount, and compare the Rule of 72 estimate to the exact answer with once-per-year compounding.
Rule of 72 formula
The rule of 72 formula is two reciprocal shortcuts. Use years to double when you know an annual return; use rate to double when you know a time goal. Both assume a fixed rate and compound growth — the calculator adds the exact annual-compound answer beside each estimate.
Years to double and rate to double
Years to double ≈ 72 ÷ annual rate (%)Required rate (%) ≈ 72 ÷ yearsExample (years): 8% → 72 ÷ 8 = 9 years (exact ≈ 9.01 years with annual compounding).
Example (rate): double in 10 years → 72 ÷ 10 = 7.2% (exact ≈ 7.18%).
Exact years:ln(2) ÷ ln(1 + r) with r = rate as a decimal. Exact rate:(2^(1/years) − 1) × 100.
Pick the direction you know
Have a return %? Use years to double. Have a target number of years? Use rate to double.
Divide 72 by that number
Rate in percent goes in the denominator for years; years go in the denominator for rate.
Compare to the exact row
If the gap matters for your decision, trust the exact annual-compound line in the results panel.
How to use this calculator
Use the mode rail above the calculator to switch directions. Everything updates as you type—no submit button—including formula steps, copy, and CSV/PDF export.
Years to double
Enter an annual rate (%). The hero shows Rule of 72 years; the breakdown shows exact years and the gap.
Rate to double
Enter target years to see the estimated % return needed to double, plus the exact annual-compound rate.
Presets
Load 4%–10% return chips or 5, 7, 10, 12 year targets, then edit for your scenario.
Export & starting amount
Optional starting balance (years mode) and CSV/PDF export for class notes or planning — free, no account.
Quick tip
Have a return %? Use Years to double. Have a deadline (e.g. “double in 10 years”)? Use Rate to double. If the rate is very high (above about 20%), read the accuracy notice and lean on the exact line in the results.
Rule of 72 vs exact compound interest
The Rule of 72 is a compound interest teaching shortcut: it approximates how long it takes for (1 + r)t = 2 when compounding happens once per year. It is not the same as simple interest, which does not reinvest earnings — for that, use our simple interest calculator.
When the estimate is close
The shortcut is usually closest for annual rates around 6%–10%. Illustrative gaps (annual compounding):
- 6% — estimate 12.00 y vs exact 11.90 y
- 8% — estimate 9.00 y vs exact 9.01 y
- 12% — estimate 6.00 y vs exact 6.12 y
- 18% — estimate 4.00 y vs exact 4.19 y
Above about 20%, the error grows — this page shows a notice and highlights the exact years or rate. For balances, contributions, or monthly compounding, use the compound interest calculator or CAGR calculator for realized growth over a date range.
Why 72?
Doubling means solving (1 + r)t = 2. Taking natural logs gives t = ln(2) ÷ ln(1 + r). For small-to-moderate r, ln(1 + r) ≈ r (as a decimal), so t ≈ 0.693 ÷ r. Express r as a percent and you get a numerator near 69.3; rounding to 72 trades a little accuracy for easy mental division (72 has many small divisors: 2, 3, 4, 6, 8, 9, 12).
Rule of 70 and Rule of 69.3
Rule of 70 — divide 70 by the rate; slightly conservative for many textbook rates.
Rule of 69.3 — uses ln(2) × 100 ≈ 69.3; often taught for continuous compounding where growth is ert.
This calculator shows the familiar 72 estimate and an exact annual-compound result. To estimate tripling time, some texts use 114 the same way (114 ÷ rate)—a related shortcut, not built into this tool.
Rule of 72 examples
Common years to double money examples—Rule of 72 first, then the exact time with once-per-year compounding. Tap a matching preset in the calculator to check your own inputs.
- 4% → 18 years (exact ≈ 17.67 years)
- 6% → 12 years (exact ≈ 11.90 years)
- 7% → ≈ 10.3 years (exact ≈ 10.24 years)
- 8% → 9 years (exact ≈ 9.01 years)
- 10% → 7.2 years (exact ≈ 7.27 years)
- 12% → 6 years (exact ≈ 6.12 years)
- Double in 5 years → rate ≈ 14.4% (exact ≈ 14.87%)
Rule of 72 calculator with a starting amount
The Rule of 72 answers how long or what rate — not the dollar ending balance by itself. If you add an optional starting amount in Years to double mode, we show the balance at the exact doubling time (for example, $10,000 becomes $20,000 when the investment has fully doubled under annual compounding).
The shortcut years are the same whether you start with $100 or $1,000,000; only the doubled dollar figure changes. For month-by-month growth or recurring deposits, use the compound interest calculator.
Limitations: taxes, fees, and variable returns
The Rule of 72 assumes a fixed annual return compounded once per year. Real portfolios swing year to year, funds charge expense ratios, and taxes can reduce what you keep. A “7% average” story is not the same as 7% every single year — sequence of returns matters when you add or withdraw money.
Use the estimate for teaching and quick comparisons; use the exact row on this page when you need precision under that assumption. For purchasing-power loss over time, see our inflation calculator (a different question than investment doubling).
Monthly rates and the Rule of 72
The rule applies to whatever period you plug in. If you enter a monthly rate (%), the answer is in months — divide by 12 if you want years. This calculator defaults to a nominal annual rate compounded once per year, which matches most textbook Rule of 72 examples.
Worked example (period consistency)
Suppose a balance compounds at 1% per month (not the same as 12% per year with monthly compounding). Rule of 72 in months: 72 ÷ 1 = 72 months to double ≈ 6 years.
If your bank quotes APY with monthly compounding, convert to a single annual assumption first — our APY calculator helps — or model the balance in the compound interest calculator.
Rule of 72 and debt
The Rule of 72 is usually taught for investments, but the same doubling logic applies when interest accrues on debt you are not paying down. Think of it as a rough “how fast could this balance grow?” check—not a payment plan.
Doubling works both ways
Credit card example: 18% APR → 72 ÷ 18 ≈ 4 years for an unpaid balance to double if interest compounds on the full balance (simplified).
Student or personal loan: use the quoted annual rate the same way for a teaching estimate; real loans amortize with each payment.
Model payments and payoff dates with our amortization schedule calculator or debt payoff calculator. For finance charges on cards, see the finance charge calculator.
Rule of 72 in Excel and Google Sheets
Put the annual rate in percent in A1 and years to double in B1 when solving the reverse direction. The same formulas work in Microsoft Excel and Google Sheets.
Formulas to copy
Estimate years:=72/A1
Exact years (annual compound):=LN(2)/LN(1+A1/100)
Estimate rate (%):=72/B1
Exact rate (%):=(2^(1/B1)-1)*100
Optional: Excel’s RATE(nper, pmt, pv, fv) can solve for a periodic rate when you also set payment and present value — for plain doubling with no cash flows, the formulas above are enough.
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Frequently asked questions about this Rule of 72 calculator
How do you calculate the Rule of 72?
Years to double ≈ 72 ÷ annual interest rate (%). To work backward, rate (%) ≈ 72 ÷ years. Example: 8% → 72 ÷ 8 = 9 years (estimate). This calculator also shows the exact once-per-year compound answer beside the shortcut.
Does the Rule of 72 actually work?
Yes, as a rough estimate—not a guarantee. It is usually closest for moderate annual rates (often around 6%–10%). At very high rates the gap widens; compare the Rule of 72 line to the exact result on this page.
What is the Rule of 72 formula?
Years to double ≈ 72 ÷ annual interest rate (%) and required rate (%) ≈ 72 ÷ years. Example: at 6%, 72 ÷ 6 = 12 years (estimate). The exact annual-compound formulas are ln(2) ÷ ln(1 + r) for years and (2^(1/years) − 1) × 100 for rate—this calculator shows both shortcut and exact results.
How long does it take to double money at 6%?
About 12 years with the Rule of 72 (72 ÷ 6). With annual compounding, the exact time is about 11.90 years.
How long does it take to double money at 7%?
About 10.3 years with the Rule of 72 (72 ÷ 7). With annual compounding, the exact time is about 10.24 years.
How long does it take to double money at 8%?
About 9 years with the Rule of 72 (72 ÷ 8). The exact annual-compound time is about 9.01 years.
How long does it take to double money at 10%?
About 7.2 years with the Rule of 72 (72 ÷ 10). With annual compounding, the exact time is about 7.27 years—the common shorthand behind “double every seven years” at roughly 10% return.
How long does it take $10,000 to double at 7%?
Doubling time does not depend on the starting balance. Rule of 72: about 10.3 years; exact annual compounding: about 10.24 years. At that exact time, $10,000 grows to about $20,000. Enter 10000 in the optional starting amount field to see the doubled balance on this page.
Can you use the Rule of 72 for inflation?
Yes, as a teaching shortcut: if prices rise at a steady annual rate, 72 ÷ inflation% estimates how long until the price level doubles. That is not a forecast of your personal budget.
Inflation erodes purchasing power; investment doubling is a separate question. Model CPI-style scenarios with our inflation calculator.
What interest rate doubles money in 5 years?
About 14.4% per year with the Rule of 72 (72 ÷ 5). Exact annual compounding requires about 14.87%.
What rate doubles money in 10 years?
About 7.2% per year with the Rule of 72 (72 ÷ 10). Exact annual compounding is about 7.18%.
Why do we use 72 and not 70 or 69.3?
72 is a convenient rounding of the natural-log approximation for doubling. 70 is another common shortcut; 69.3 is sometimes used for continuous compounding. Any of them are estimates — use the exact line when precision matters.
Rule of 72 vs compound interest calculator — which should I use?
Use the Rule of 72 when you only need doubling time or a required rate under a simple annual assumption. Use a compound interest calculator when you need an ending balance, recurring contributions, or monthly/quarterly compounding—see our compound interest calculator.
Can you use the Rule of 72 with monthly interest?
Yes. If you plug in a monthly rate (%), the answer is in months (divide by 12 for years). This calculator defaults to a nominal annual rate compounded once per year.
For monthly compounding on a dollar balance, use our compound interest calculator or APY calculator.
Is it true your 401(k) doubles every 7 years?
Not automatically. That rule of thumb fits only if already-invested money earns about 10% per year on average (72 ÷ 10 ≈ 7.2 years), with no new contributions, fees, or bad years in the mix.
Real 401(k) paths include deposits, employer match, expense ratios, and volatility. Use our 401(k) calculator for projection-style math.
Can you use the Rule of 72 for debt?
The same doubling idea applies to how fast a balance grows at a steady APR — for example, 18% → about 4 years to double an unpaid balance in a simplified model. Real loans have minimum payments and amortization.
Treat this page as a teaching shortcut; model loans with our amortization schedule or debt payoff calculator.
How do you use the Rule of 72 in Excel?
Put the annual rate (%) in A1 and years to double in B1. Estimate years: =72/A1. Exact years: =LN(2)/LN(1+A1/100). Estimate rate: =72/B1. Exact rate (%): =(2^(1/B1)-1)*100. The same formulas work in Google Sheets.
Is this Rule of 72 calculator financial advice?
No. It is an educational math tool for doubling-time estimates under the assumptions shown on the page. Check official statements or talk with a qualified professional before investing or borrowing.